【Inkjet】🖨️ 02. inkjet-timing: Visualizing Temporal Causality in Piezoelectric Inkjet Systems

topics: [“inkjet”, “control engineering”, “physical modeling”, “visualization”, “aitl”]

📌 Introduction

At first glance, a piezoelectric inkjet system may appear simple:
apply a waveform and a droplet is ejected.

In reality, however, it is a system in which multiple physical domains—

• Electrical (V–I)
• Mechanical (displacement)
• Fluidic (pressure and flow)

—are causally connected on a shared microsecond-scale time axis.

This article introduces inkjet-timing,
a visualization project designed to make this temporal causality intuitive.

🧩 What Is inkjet-timing?

inkjet-timing is an educational / PoC project that visualizes:

“How electrical, mechanical, and fluid phenomena are causally connected
along the same time axis in piezoelectric inkjet ejection.”

The focus is not numerical accuracy or CFD-level reproduction, but:

• Temporal order
• Delay
• Phase relationships
• Flow of causality

📊 What Is Visualized

A single shared time axis is used, with signals stacked vertically:

• Drive voltage V(t)
• Current response I(t)
• Piezoelectric displacement Δx(t)
• Channel pressure P(t)
• Ink flow rate Q(t) (outflow / inflow)

Each waveform belongs to a different physical domain,
yet all are linked by temporal causality.

What matters is not the absolute value, but:

Which phenomenon rises first, and in what order.

🧠 Why This Is Not PID Control

Inkjet droplet ejection is characterized by:

• Fully open-loop operation
• Feed-forward driving
• Completion within a few microseconds

There is no time to run feedback control
during droplet formation.

Stability is instead physically embedded through:

• Drive waveform design
• Mechanical damping
• Acoustic and fluidic structures

This places inkjet actuation in a different category
from PID-based feedback control.

🧭 Design Intent

This visualization is designed under the following assumptions:

• Not CFD (qualitative, not quantitative)
• Causal structure prioritized over parameter precision
• Representation of a normally operating overdamped system

The goal is not numerical prediction, but:

“Why does this phenomenon occur at this timing?”

—enabling rapid acquisition of physical intuition.

📐 How to Read the Visualization

• Horizontal axis: time (microsecond scale)
• Vertical axis: physical domains (top to bottom: electrical → mechanical → fluid)
• A single time cursor penetrates all domains
• Each domain’s marker represents the instantaneous state

It can be understood as:

An oscilloscope extended across physical domains

rather than signals alone.

🔗 Live Demo (GitHub Pages)

An interactive browser-based demo is publicly available:

👉 https://samizo-aitl.github.io/inkjet-timing/index.html

• No installation required
• Fully browser-based
• Adjustable gains and timing
• Intended for education, explanation, and design reviews

🧩 Positioning Within AITL

In AITL (Architecture-Integrated Thinking Loop):

• PID: real-time feedback control
• FSM: state transition management
• Physical design: embedded stability

inkjet-timing represents a class of systems where:

• Behavior is determined by structure and timing
• Stability is inherent in physical design
• Causal relationships must be viewed holistically

Inkjet waveform design can thus be framed as:

A feed-forward control problem under strict physical constraints

📜 License

Code

Source code including HTML, JavaScript, and CSS
is released under the MIT License.

Conceptual Model and Explanations

Physical interpretation, causal structure, and design philosophy
are provided for educational and research purposes.

When reusing the conceptual model or methodology,
appropriate attribution is requested.

📝 Closing Remarks

This project is intentionally simplified.

It is not:

• A replacement for detailed simulation
• A production optimization tool

However, with respect to a single point—

“Seeing time and causality correctly”

—it significantly advances understanding of inkjet system design.

GitHub Repository
https://github.com/Samizo-AITL/inkjet-timing